Question 818929
{{{324^"1/4"/4^"-1/4"=324^(1/4)*4^(1/4)=(324*4)^(1/4)}}}
Now, I could write it as {{{root(4,324*4)}}} ,
but I prefer to write it with the fractional exponent.
At this point, I start factoring.
I know that {{{4=2^2}}} ,
but I have to work a bit to factor {{{324}}} .
So I try dividing it by {{{2}}} and see that
324 ÷ 2 = 162 and 162 ÷ 2 = 81,
so {{{324=2*2*81=2^2*81}}} ,
and since I know that {{{81=9^2=3^4}}} ,
I can write the prime factorization as
{{{324=2^2*3^4}}}
So 
{{{324^"1/4"/4^"-1/4"=324^(1/4)*4^(1/4)=(324*4)^(1/4)=(2^2*3^4*2^2)^(1/4)=(2^4*3^4)^(1/4)}}} = {{{((2*3)^4)^"1/4"=6^(4*"1/4")=6^1=highlight(6)}}} .
You may prefer to write it as
{{{324^"1/4"/4^"-1/4"=324^(1/4)*4^(1/4)=(324*4)^(1/4)=root(4,1296)=highlight(6)}}} for short.
(I just wrote it as I thought about it, and as I calculated it with pencil and paper. With a calculator, I can calculate {{{324*4=1296}}},
and {{{root(4,1296)=sqrt(sqrt(1296))=6}}} , but I prefer to factor and use paper, because that way there is no chance of pressing the wrong key).